1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two representation

  1. Jan 8, 2014 #1
    1. The problem statement, all variables and given/known data
    ##e = \begin{bmatrix}
    1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##,
    ##a =\frac{1}{2} \begin{bmatrix}
    1 & -\sqrt{3} \\[0.3em]
    -\sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##.
    ##b =\frac{1}{2} \begin{bmatrix}
    1 & \sqrt{3} \\[0.3em]
    \sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    ##c= \begin{bmatrix}
    -1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##
    ##d=\frac{1}{2} \begin{bmatrix}
    -1 & \sqrt{3} \\[0.3em]
    -\sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    ##f=\frac{1}{2} \begin{bmatrix}
    -1 & -\sqrt{3} \\[0.3em]
    \sqrt{3} & -1 \\[0.3em]

    \end{bmatrix}##
    This is irreducible representation of group ##S_3##. \\
    Reducible representation of ##S_3## is
    ##e=d=f = \begin{bmatrix}
    1 & 0 \\[0.3em]
    0 & 1 \\[0.3em]

    \end{bmatrix}##
    ##a =b=c=\frac{1}{2} \begin{bmatrix}
    -1 & -\sqrt{3} \\[0.3em]
    -\sqrt{3} & 1 \\[0.3em]

    \end{bmatrix}##
    Why is better to use irreducible then reducible representation in this case and in general?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 8, 2014 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What do you mean by "better to use?" You haven't used any representations to do anything.
     
  4. Jan 9, 2014 #3
    In practice one always take some irreducible representation to work with. My question is why?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Two representation
  1. Base representation ~ (Replies: 1)

  2. Representation theory (Replies: 0)

  3. Series representation (Replies: 3)

Loading...